Multiple event probability

Hi, for some reason I'm having issues with something I usually find easy. The question is as follows:

events A and B are such that P(A) = 2/5, P(B)= 1/2 and P(A|B') = 4/5

Find

a.) P(A n B')
b.) P(A n B)
c.) P(A u B)
d.) P(A|B)

next, state with reason, whether or not A and B are

a) Mutually exclusive
b) independent

What I've done:

When I try and draw out a Venn diagram (As i find them helpful for displaying data) can get P(A) to equal 4/5 when given B' however when I try and work out P(A n B) for the middle of the Venn diagram it comes out as 0.2, when subtracting that from the probabilities of A and B I end up with 0.2 for A. Which no matter what I do I can't make P(A|B') equal 4/5. So I can make my Venn diagram work and I have no idea whether to use the values without subtracting (A n B) or not. I was wondering if they were independent and there were no cases where they are both chosen so P(A n B) would = 0?

Please help it would be much appreciated. I look forward to hearing from you!

Re: Multiple event probability

Hi, for some reason I'm having issues with something I usually find easy. The question is as follows:

events A and B are such that P(A) = 2/5, P(B)= 1/2 and P(A|B') = 4/5

Find

a.) P(A n B')
b.) P(A n B)
c.) P(A u B)
d.) P(A|B)

next, state with reason, whether or not A and B are

a) Mutually exclusive
b) independent

What I've done:

When I try and draw out a Venn diagram (As i find them helpful for displaying data) can get P(A) to equal 4/5 when given B' however when I try and work out P(A n B) for the middle of the Venn diagram it comes out as 0.2, when subtracting that from the probabilities of A and B I end up with 0.2 for A. Which no matter what I do I can't make P(A|B') equal 4/5. So I can make my Venn diagram work and I have no idea whether to use the values without subtracting (A n B) or not. I was wondering if they were independent and there were no cases where they are both chosen so P(A n B) would = 0?

Please help it would be much appreciated. I look forward to hearing from you!